Energy spectra and localized states with potential V/γ₀ = 0.00. The spectra of a single particle in the zigzag bilayer graphene nanoribbons with a line defect located at n_y0 = 120 on the upper layer is shown in Fig. 1(b), which has PBC along the y direction. (a) Energy spectrum near E(k_x) = 0, where the red and green lines denote the defect states of the graphene with a line-defect. The blue dot indicates an energy state with E(k_x) = 0. Panel (b) shows the particle-distribution of the zero-energy energy state indicated by the blue dot in panel (a) on the upper layer (blue solid line) and lower layer (red solid line), respectively.